A calculation method for geological disaster collapse and landslide monitoring based on the integration of Beidou and millimeter-wave radar

Abstract

The present invention relates to the field of geological disaster monitoring technology, and discloses a geological disaster collapse and landslide monitoring calculation method that integrates Beidou and millimeter-wave radar, comprising the following steps: S1, obtaining millimeter-wave radar ranging data and Beidou differential observation data; S2, constructing a state space model for Beidou / millimeter-wave radar data fusion positioning; S3, determining Beidou double-difference ambiguity based on Beidou / millimeter-wave radar fusion data; and S4, determining the real-time deformation of the monitoring point. Dynamic quality control of Beidou observation data is performed through millimeter-wave radar to eliminate data with severe noise and multipath effects, thereby ensuring the validity and accuracy of the data. Then, through the accuracy assessment of millimeter-wave observation data and Beidou data, a joint random model is established to improve the overall solution accuracy of the fused data. In the event that the Beidou signal is blocked or missing, the continuity and reliability of geological disaster monitoring are ensured by relying solely on millimeter-wave radar observation data and solving the problem through epoch recursion.

Description

Technical Field

[0001] The present invention relates to the field of geological disaster monitoring technology, and specifically to a geological disaster collapse and landslide monitoring calculation method integrating Beidou and millimeter wave radar. Background Art

[0002] With the increasing frequency of geological disasters, especially sudden geological disasters such as collapses and landslides, obtaining high-precision, real-time monitoring data has become an important means of protecting life and property. Currently, geological disaster monitoring mainly relies on positioning methods such as the Beidou satellite navigation system and GPS, combined with multi-sensor fusion methods to improve monitoring accuracy.

[0003] For example, the Chinese patent authorization announcement number is: CN115325928B, and the authorization announcement date is: 2023.01.31. This patent discloses a comprehensive monitoring system for landslide surface cracks based on Beidou communication, including a layout module, a monitoring module, an early warning module and a monitoring module; and a landslide offset threshold is set according to the landslide's own information, and the landslide offset threshold is used to determine whether the monitoring point position is within the normal area. If the landslide offset exceeds the threshold, it means that the monitoring point cannot monitor the landslide area well at this time, and the monitoring point needs to be rearranged according to the offset direction; on the one hand, it can ensure the accuracy of monitoring point monitoring and avoid invalid monitoring of monitoring points. On the other hand, it can also timely conduct secondary monitoring of the landslide according to the landslide offset.

[0004] A single Beidou system is susceptible to signal blocking and multipath effects in complex geological environments, resulting in noise and errors in the observation data, making it impossible to stably obtain high-precision deformation monitoring results. Many researchers have tried to introduce other sensors, such as accelerometers and lidar, to integrate with the Beidou system, but the performance of these sensors is still limited in harsh environments.

[0005] Millimeter-wave radar, as a sensor with high penetration and environmental adaptability, can effectively supplement the shortcomings of Beidou signals in complex environments. Therefore, fusing the Beidou system with millimeter-wave radar can effectively improve the accuracy and reliability of geological disaster monitoring. However, there is currently a lack of effective solution methods for the fusion of Beidou and millimeter-wave radar data. In particular, how to control data quality, evaluate data accuracy, and establish a stochastic model suitable for geological disaster monitoring during the data fusion process is a major shortcoming in the existing technology. Based on this, this application proposes a geological disaster landslide monitoring calculation method that integrates Beidou and millimeter-wave radar to solve the above problems. Summary of the Invention

[0006] (1) Technical problems solved

[0007] In response to the shortcomings of the existing technology, the present invention provides a geological disaster collapse and landslide monitoring and calculation method that integrates Beidou and millimeter-wave radar. The geological disaster collapse and landslide monitoring and calculation method that integrates Beidou and millimeter-wave radar uses millimeter-wave radar to dynamically control the quality of Beidou observation data, eliminates data with severe noise and multipath effects to ensure the validity and accuracy of the data, and then establishes a joint random model through the accuracy assessment of millimeter-wave observation data and Beidou data to improve the overall solution accuracy of the fused data.

[0008] (2) Technical solution

[0009] To achieve the above objectives, the present invention provides the following technical solution: a method for geological disaster landslide monitoring and calculation by integrating Beidou and millimeter wave radar, comprising the following steps:

[0010] S1. Obtain millimeter-wave radar ranging data and Beidou differential observation data;

[0011] S2. Construct a state space model for BeiDou / millimeter wave radar data fusion positioning;

[0012] S3, Beidou double-difference ambiguity determination based on Beidou / millimeter-wave radar fusion data;

[0013] S4. Determine the real-time deformation of the monitoring point.

[0014] Preferably, the specific steps of obtaining millimeter wave radar ranging data and Beidou differential observation data in step S1 are as follows:

[0015] (1) The spatial rectangular coordinates X of the target point T near the known monitoring station T , use the millimeter wave radar installed at the monitoring station to measure the geometric distance from the equipment to point T in real time, and record the distance measured by the millimeter wave radar at time k as S k ;

[0016] (2) Using the BeiDou signal receiving equipment installed at the monitoring station to receive BeiDou positioning observation data and differential enhancement data broadcast by the surrounding ground-based enhancement base stations, the spatial rectangular coordinates X of the base station are obtained. B At the same time, the synchronous observation data of the monitoring station and the reference station are subjected to inter-station difference and inter-satellite difference in real time to obtain pseudo-range and phase observation values of the station-satellite double difference. If the number of Beidou double-difference satellites at time k is n k , then the double-difference pseudo-range observation value at time k is recorded as Carrier phase observations

[0017] Preferably, the specific steps of constructing the state space model of Beidou / millimeter wave radar data fusion positioning in step S2 are as follows:

[0018] (1) Construct the state equation for BeiDou / millimeter-wave radar data fusion positioning;

[0019] (2) Constructing the observation equations for BeiDou data;

[0020] (3) Constructing the length-constrained observation equation for millimeter-wave radar data;

[0021] (4) Constructing the joint observation equation for BeiDou / millimeter-wave radar data fusion positioning;

[0022] (5) Determine the random model of Beidou + millimeter wave radar data fusion positioning.

[0023] Preferably, the steps of constructing the state equation for Beidou / millimeter wave radar data fusion positioning are as follows:

[0024] The double-difference carrier phase observations of the monitoring station relative to the reference station at time k-1 and time k are differentiated between epochs to obtain triple-difference phase observations; the triple-difference observation equation is then constructed, and the baseline change dX of the monitoring station relative to the reference station from time k-1 to time k is obtained by single-epoch least squares solution. k-1，k and its variance D dX ;

[0025] The state equation for constructing Beidou + millimeter wave radar data fusion positioning is as follows:

[0026] X k =X k-1 +ΔX k-1，k (1) In the formula, X k =(b k , N k ) T is the state parameter of the model, where b k =(dx k ,dy k , dz k ) is the baseline position parameter of the monitoring station relative to the reference station at time k, is the double difference ambiguity parameter at time k. k-1，k =(dX k-1，k ,dN k-1，k ) T , where dN k-1，k is the change of double difference ambiguity between time k-1 and time k. When no cycle slip occurs, this term is n k A zero-valued row vector of elements.

[0027] Preferably, the steps of constructing the observation equation of Beidou data are as follows:

[0028] Using the double-difference pseudorange observation value P at time k k and carrier phase observations The double-difference pseudorange and carrier phase observation equations are constructed as follows:

[0029] Where λ is the wavelength of the carrier phase, H1 is n k 3 rows and 3 columns of coefficient matrix, 01 is n k row n k Column zero value matrix, I is n k row n k Column identity matrix. Δ P and are the pseudorange and carrier phase observation residuals, respectively.

[0030] Preferably, the steps of constructing the length constraint observation equation of millimeter wave radar data are as follows:

[0031] Considering the unknown coordinates X of the monitoring station M =b k +X B , the known coordinates X of the target point T T And the distance S between the two points measured by the millimeter wave radar k , construct the length constraint observation equation as follows:

[0032] S k =‖X M -X T ‖=‖b k +X B -X T ‖ (3) In the formula, ‖*‖ is the quadratic norm. Linearize the above formula and we get

[0033] S k =H2b k +Δ S (4) where H2 is the linearized 1-row 3-column Jacobian matrix, Δ S is the residual of the millimeter-wave radar ranging value.

[0034] Preferably, the steps of constructing the joint observation equation for Beidou / millimeter wave radar data fusion positioning are as follows:

[0035] Combining equations (2) and (4), we obtain the observation equation for BeiDou / millimeter-wave radar data fusion positioning:

[0036] Where 02 is n k a zero-valued row vector of elements;

[0037] The steps for determining the random model for Beidou + millimeter wave radar data fusion positioning are as follows:

[0038] For the state space model, the system noise variance of its state equation is the baseline variation variance D of the state equation for constructing BeiDou / millimeter wave radar data fusion positioning. dX The measurement noise of the pseudorange and carrier phase observation values in the observation equation adopts a variance model based on the altitude angle and double difference correlation, and the standard deviations of the measurement noise of the non-differenced pseudorange and carrier phase are 0.3m and 0.002 weeks respectively. The variances of the double difference pseudorange and carrier phase measurement noise are D P and The measurement noise of the millimeter-wave radar ranging value in its observation equation adopts the following error model:

[0039]

[0040] Where σ0 is the fixed error of millimeter-wave radar ranging, and K is the proportional error coefficient of millimeter-wave radar ranging. The specific values of the two can be determined by the performance of the actual millimeter-wave radar equipment used. The measurement variance of the joint observation equation is

[0041]

[0042] Preferably, the Beidou double-difference ambiguity determination steps based on Beidou / millimeter-wave radar fusion data are as follows:

[0043] (1) Using the extended Kalman filter to calculate the floating-point solution of the ambiguity, the state equation (1), the observation equation (5) and the stochastic model (7) are combined to perform the Kalman filter solution to obtain the floating-point solution of the model state parameters. and its variance matrix

[0044] (2) Using the obtained model state parameters and their variance matrix, the optimal group fuzziness is obtained through the LAMBDA search algorithm and the quadratic form of the ambiguity residual R. Then, the Ratio test is performed on the optimal group of ambiguities. If R ≥ 3.0, the ambiguity is considered to be correctly fixed.

[0045] Preferably, the steps of determining the real-time deformation amount of the monitoring point are as follows:

[0046] (1) Using fixed ambiguity integer values Substituting the observation equation (5) of fusion positioning and removing the pseudo-range observation equation, the observation equation of the fixed solution is obtained as follows:

[0047] The corresponding measurement variance is Solve the above equation with least squares to obtain the precise baseline position of the monitoring station relative to the reference station at time k According to the precise coordinates X of the base station B , calculate the real-time position of the monitoring point at time k

[0048] (2) Using the coordinate time series of monitoring points at different times Calculate the real-time deformation of the monitoring point

[0049] (3) Beneficial effects

[0050] Compared with the existing technology, the present invention provides a geological disaster landslide monitoring and calculation method that integrates Beidou and millimeter wave radar, which has the following beneficial effects:

[0051] This method for geological disaster landslide monitoring, integrating Beidou and millimeter-wave radar, uses millimeter-wave radar to dynamically control Beidou observation data, eliminating data with severe noise and multipath effects to ensure data validity and accuracy. Subsequently, through accuracy assessment of both millimeter-wave and Beidou data, a joint stochastic model is established to improve the overall accuracy of the fused data. Based on this stochastic model, an extended Kalman filter is used to fuse and resolve Beidou and millimeter-wave radar data, generating high-precision, real-time geological disaster monitoring data. In the event of Beidou signal obstruction or loss, the method relies solely on millimeter-wave radar observation data, using epoch-by-epoch recursive resolution to ensure the continuity and reliability of geological disaster monitoring. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] Figure 1 It is a schematic diagram of the solution of the present invention;

[0053] Figure 2 It is a calculation flow chart of the present invention. DETAILED DESCRIPTION

[0054] The following will be combined with the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the embodiments described are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0055] See also Figure 1-2 The present invention provides a method for geological disaster landslide monitoring and calculation by integrating Beidou and millimeter-wave radar. The method is intended to be applied to the positioning and calculation of landslide geological disaster monitoring by integrating Beidou carrier phase observation data and millimeter-wave radar ranging data to solve the problem of low data calculation accuracy in complex geological environments in the existing technology. Specifically, the method includes the following steps:

[0056] S1. Obtain millimeter-wave radar ranging data and Beidou differential observation data;

[0057] S2. Construct a state space model for BeiDou / millimeter wave radar data fusion positioning;

[0058] S3, Beidou double-difference ambiguity determination based on Beidou / millimeter-wave radar fusion data;

[0059] S4. Determine the real-time deformation of the monitoring point.

[0060] The specific steps for obtaining millimeter-wave radar ranging data and Beidou differential observation data in step S1 are as follows:

[0061] (1) The spatial rectangular coordinates X of the target point T near the known monitoring station T , use the millimeter wave radar installed at the monitoring station to measure the geometric distance from the equipment to point T in real time, and record the distance measured by the millimeter wave radar at time k as S k ;

[0062] (2) Using the BeiDou signal receiving equipment installed at the monitoring station to receive BeiDou positioning observation data and differential enhancement data broadcast by the surrounding ground-based enhancement base stations, the spatial rectangular coordinates X of the base station are obtained. B At the same time, the synchronous observation data of the monitoring station and the reference station are subjected to inter-station difference and inter-satellite difference in real time to obtain pseudo-range and phase observation values of the station-satellite double difference. If the number of Beidou double-difference satellites at time k is n k , then the double-difference pseudo-range observation value at time k is recorded as Carrier phase observations

[0063] The specific steps for constructing the state space model of Beidou / millimeter wave radar data fusion positioning in step S2 are as follows:

[0064] (1) Construct the state equation for BeiDou / millimeter-wave radar data fusion positioning;

[0065] The double-difference carrier phase observations of the monitoring station relative to the reference station at time k-1 and time k are differentiated between epochs to obtain triple-difference phase observations. The triple-difference observation equation is then constructed and the baseline change dX of the monitoring station relative to the reference station from time k-1 to time k is obtained by single-epoch least squares solution. k-1，k and its variance D dX The state equation for BeiDou + millimeter-wave radar data fusion positioning is constructed as follows:

[0066] X k =X k-1 +ΔX k-1,k (1) In the formula, X k =(b k ,N k ) T is the state parameter of the model, where b k =(dx k ,dyk ,dz k ) is the baseline position parameter of the monitoring station relative to the reference station at time k, is the double difference ambiguity parameter at time k. k-1,k =(dX k-1 ,dN k-1,k ) T , where dN k-1,k is the change of double difference ambiguity between time k-1 and time k. When no cycle slip occurs, this term is n k A zero-valued row vector of elements.

[0067] (2) Constructing the observation equations for BeiDou data;

[0068] Using the double-difference pseudorange observation value P at time k k and carrier phase observations The double-difference pseudorange and carrier phase observation equations are constructed as follows:

[0069] Where λ is the wavelength of the carrier phase, H1 is n k 3 rows and 3 columns of coefficient matrix, 01 is n k row n k Column zero value matrix, I is n k row n k Column identity matrix. Δ P and are the pseudorange and carrier phase observation residuals, respectively.

[0070] (3) Constructing the length-constrained observation equation for millimeter-wave radar data;

[0071] Considering the unknown coordinates X of the monitoring station M =b k +X B , the known coordinates X of the target point T T And the distance S between the two points measured by the millimeter wave radar k , construct the length constraint observation equation as follows:

[0072] S k =||X M -X T ||=||b k +X B -X T || (3)In the formula, ||*|| is the quadratic norm.

[0073] Linearize the above formula and we get

[0074] S k =H2b k +Δ S(4) where H2 is the linearized 1-row 3-column Jacobian matrix, Δ S is the residual of the millimeter-wave radar ranging value.

[0075] (4) Constructing the joint observation equation for BeiDou / millimeter-wave radar data fusion positioning;

[0076] Combining equations (2) and (4), we obtain the observation equation for BeiDou / millimeter-wave radar data fusion positioning:

[0077] Where 02 is a zero-valued row vector of nk elements.

[0078] (5) Determine the stochastic model for BeiDou + millimeter-wave radar data fusion positioning;

[0079] For the state space model, the system noise variance of its state equation is the baseline variation variance D of the state equation for constructing BeiDou / millimeter wave radar data fusion positioning. dX The measurement noise of the pseudorange and carrier phase observation values in the observation equation adopts a variance model based on the altitude angle and double difference correlation, and the standard deviations of the measurement noise of the non-differenced pseudorange and carrier phase are 0.3m and 0.002 weeks respectively. The variances of the double difference pseudorange and carrier phase measurement noise are D P and The measurement noise of the millimeter-wave radar ranging value in its observation equation adopts the following error model:

[0080]

[0081] Where σ0 is the fixed error of millimeter-wave radar ranging, and K is the proportional error coefficient of millimeter-wave radar ranging. The specific values of the two can be determined by the performance of the actual millimeter-wave radar equipment used. The measurement variance of the joint observation equation is

[0082]

[0083] The steps for determining BeiDou double-difference ambiguity based on BeiDou / millimeter-wave radar fusion data are as follows:

[0084] (1) Using the extended Kalman filter to calculate the floating-point solution of the ambiguity, the state equation (1), the observation equation (5) and the stochastic model (7) are combined to perform the Kalman filter solution to obtain the floating-point solution of the model state parameters. and its variance matrix

[0085] (2) Using the obtained model state parameters and their variance matrix, the optimal group fuzziness is obtained through the LAMBDA search algorithm and the quadratic form of the ambiguity residual R. Then, the Ratio test is performed on the optimal group of ambiguities. If R ≥ 3.0, the ambiguity is considered to be correctly fixed.

[0086] The steps to determine the real-time deformation of the monitoring point are as follows:

[0087] (1) Using fixed ambiguity integer values Substituting the observation equation (5) of fusion positioning and removing the pseudo-range observation equation, the observation equation of the fixed solution is obtained as follows:

[0088] The corresponding measurement variance is Solve the above equation with least squares to obtain the precise baseline position of the monitoring station relative to the reference station at time k According to the precise coordinates X of the base station B , calculate the real-time position of the monitoring point at time k

[0089] (2) Using the coordinate time series of monitoring points at different times Calculate the real-time deformation of the monitoring point

[0090] It should be noted that the above fusion solution process uses an extended Kalman filter to dynamically adjust the weights of Beidou and millimeter wave data sources through a random model.

[0091] This method uses millimeter-wave radar to dynamically control the quality of Beidou observation data, eliminating data with severe noise and multipath effects to ensure data validity and accuracy. Subsequently, by assessing the accuracy of both millimeter-wave and Beidou data, a joint stochastic model is established to improve the overall accuracy of the fused data. Based on this stochastic model, an extended Kalman filter is used to fuse Beidou and millimeter-wave radar data to obtain high-precision, real-time geological hazard monitoring data. In the event of Beidou signal obstruction or loss, the method relies solely on millimeter-wave radar data, using epoch-by-epoch recursive solution to ensure the continuity and reliability of geological hazard monitoring.

[0092] While embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions, and variations may be made to these embodiments without departing from the principles and spirit of the invention, and that the scope of the invention is defined by the appended claims and their equivalents.

Claims

1. A method for geological disaster landslide monitoring and calculation based on the integration of Beidou and millimeter wave radar, characterized in that: The following steps are involved: S1. Obtain millimeter-wave radar ranging data and Beidou differential observation data; S2. Construct a state space model for BeiDou / millimeter wave radar data fusion positioning; S3, Beidou double-difference ambiguity determination based on Beidou / millimeter-wave radar fusion data; S4, determining the real-time deformation of the monitoring point; The specific steps of constructing the state space model of Beidou / millimeter wave radar data fusion positioning in step S2 are as follows: (1) Constructing the state equation for BeiDou / millimeter-wave radar data fusion positioning; (2) Constructing the observation equation for BeiDou data; (3) Constructing the length-constrained observation equation for millimeter-wave radar data; (4) Constructing joint observation equations for BeiDou / millimeter-wave radar data fusion positioning; (5) Determine the stochastic model for BeiDou + millimeter-wave radar data fusion positioning; The steps of determining the Beidou double-difference ambiguity based on Beidou / millimeter-wave radar fusion data are as follows: (1) Using extended Kalman filter to calculate the floating point solution of ambiguity, the joint state equation , observation equation and random model, perform Kalman filter solution to obtain the floating point solution of model state parameters and its variance matrix ; (2) Using the obtained model state parameters and their variance matrix, the optimal group fuzziness is obtained through the LAMBDA search algorithm And the ambiguity residual quadratic form R, then perform the Ratio test on the optimal group ambiguity. If , the ambiguity is considered to be correctly fixed; The steps of determining the real-time deformation of the monitoring point are as follows: (1) Using fixed ambiguity integer values , back-substitute the observation equation of fusion positioning and remove the pseudo-range observation equation, and the observation equation of the fixed solution is obtained: (8) The corresponding measurement variance is , perform the least squares solution on the above formula to obtain the precise baseline position of the monitoring station relative to the reference station at time k , according to the precise coordinates of the base station , calculate the real-time position of the monitoring point at time k ; (2) Using the coordinate time series of monitoring points at different times , calculate the real-time deformation of the monitoring point .

2. The method for geological disaster landslide monitoring and calculation based on the integration of Beidou and millimeter wave radar according to claim 1 is characterized in that: The specific steps of obtaining millimeter wave radar ranging data and Beidou differential observation data in step S1 are as follows: (1) The spatial rectangular coordinates of the target point T near the known monitoring station , use the millimeter wave radar installed at the monitoring station to measure the geometric distance from the equipment to point T in real time, and record the distance measured by the millimeter wave radar at time k as ; (2) Use the BeiDou signal receiving equipment installed at the monitoring station to receive BeiDou positioning observation data and differential enhancement data broadcast by surrounding ground-based enhancement base stations to obtain the spatial rectangular coordinates of the base station. At the same time, the synchronous observation data of the monitoring station and the reference station are subjected to inter-station difference and inter-satellite difference in real time to obtain pseudo-range and phase observation values of the station-satellite double difference. If the number of Beidou double-difference satellites at time k is , then the double-difference pseudo-range observation value at time k is recorded as , carrier phase observation value .

3. The method for geological disaster landslide monitoring and calculation based on the integration of Beidou and millimeter wave radar according to claim 2 is characterized in that: The steps for constructing the state equation for Beidou / millimeter wave radar data fusion positioning are as follows: The double-difference carrier phase observations of the monitoring station relative to the reference station at time k-1 and time k are differentiated between epochs to obtain triple-difference phase observations; the triple-difference observation equation is then constructed, and the baseline change of the monitoring station relative to the reference station from time k-1 to time k is obtained by single-epoch least squares solution. and its variance ; The state equation for constructing Beidou + millimeter wave radar data fusion positioning is as follows: ( ) Where, is the state parameter of the model, where is the baseline position parameter of the monitoring station relative to the reference station at time k, is the double difference ambiguity parameter at time k, ,in is the change of double difference ambiguity between time k-1 and time k. When no cycle slip occurs, this term is A zero-valued row vector of elements.

4. The method for geological disaster landslide monitoring and calculation based on the integration of Beidou and millimeter wave radar according to claim 3 is characterized in that: The steps for constructing the observation equation of Beidou data are as follows: Using the double-difference pseudorange observation value at time k and carrier phase observations , the double-difference pseudorange and carrier phase observation equations are constructed as follows: ( ) Where, is the wavelength of the carrier phase, for A coefficient matrix with 3 rows and 3 columns, for OK A matrix with zero columns, for OK The column identity matrix, and are the pseudorange and carrier phase observation residuals, respectively.

5. The method for geological disaster landslide monitoring and calculation based on the integration of Beidou and millimeter wave radar according to claim 4 is characterized in that: The steps for constructing the length constraint observation equation for millimeter wave radar data are as follows: Considering the unknown coordinates of the monitoring station , the known coordinates of the target point T and the distance between the two points measured by millimeter-wave radar , construct the length constraint observation equation as follows: ( ) Where, is the quadratic norm, linearize the above formula and get ( ) Where, is the linearized 1-row and 3-column Jacobian matrix, is the residual of the millimeter-wave radar ranging value.

6. The method for geological disaster landslide monitoring and calculation based on the integration of Beidou and millimeter wave radar according to claim 5 is characterized in that: The steps for constructing the joint observation equation for Beidou / millimeter wave radar data fusion positioning are as follows: Joint Japanese style , we get the observation equation for BeiDou / millimeter-wave radar data fusion positioning: ( ) Where, for a zero-valued row vector of elements; The steps for determining the random model for Beidou + millimeter wave radar data fusion positioning are as follows: For the state space model, the system noise variance of its state equation is the baseline variation variance of the state equation for constructing BeiDou / millimeter wave radar data fusion positioning ; The measurement noise of the pseudorange and carrier phase observation values in the observation equation adopts a variance model based on the altitude angle and double difference correlation, and the standard deviations of the measurement noise of the undifferenced pseudorange and carrier phase are 0.3m and 0.002 weeks respectively. The measurement noise variances of the double difference pseudorange and carrier phase are and ; The measurement noise of the millimeter-wave radar ranging value in its observation equation adopts the following error model: ( ) Where, is the fixed error of millimeter wave radar ranging, is the proportional error coefficient of millimeter-wave radar ranging. The specific values of the two can be determined by the performance of the actual millimeter-wave radar equipment used. The measurement variance of the joint observation equation is ( )。

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